The Natural Semantics of Quantifiers
Publication Year: 2011
Published by: The MIT Press
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Title Page, Copyright
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This book is about the syntax and semantics of quantifier-scope, in interaction with (among other constructions) negation, polarity, coordination, and pronominal binding. It does not consider the ramifications of intensional scope and “opacity,” although I hope that the basic apparatus outlined here will be naturally extendable in that direction. ...
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The research described in this book began when I taught at the University of Pennsylvania, in conversations with Jong Park, whose doctoral dissertation (1996) represented the first attempt on this problem in a CCG framework and provided a catalyst to the present work. Some of the ideas presented here (including the use of generalized Skolem terms) were first advanced in embryonic ...
Chapter 1 Prologue
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Like many other phenomena whose importance might seem to a linguist to be self-evident, the formal semantics of quantification is nowadays largely ignored by the computational linguists and psycholinguists most concerned with the practicalities of building devices that retrieve information from text on the web, and explaining human language performance. For such purposes, it often ...
Chapter 2 Introduction
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... The Montagovian assumption of “direct” or “surface” compositional semantics (Montague 1970a; Hausser 1984; Jacobson 1996a) requires that all available readings of this kind should arise directly from the combinatorics of syntax operating over the lexical elements and their meanings. However, the traditional grammar of English offers only a single syntactic structure for the ...
Part I Natural Semantics
Chapter 3 The Natural History of Scope
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Linking semantic scope directly to syntactic combinatorics makes it possible to explain a number of asymmetries between and among the scope-taking possibilities for universal and existential nominals in interaction with natural language syntax. These asymmetries present a challenge to all frameworks that attempt to capture scope phenomena in terms of uniform operations over generalized ...
Chapter 4 Semantics without Existential Quantifiers
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The inclusion of the generalized form of Skolem terms introduced in the last chapter brings a number of benefits to the semantics. It also avoids numerous paradoxes that arise when natural language quantifiers are represented by traditional existential quantifiers, ranging from the apparently anomalous scope of indefinites in donkey sentences to certain long-standing puzzles ...
Chapter 5 Model Theory
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A model theory for the present calculus is provided by adapting a standard statically scoped model theory for first-order logic (Robinson 1974). The presentation here does not cover intensional relations, although some examples elsewhere in the book include verbs of propositional attitude. The ultimate intention is to generalize the model theory defined here to the case of relations ...
Part II Natural Grammar
Chapter 6 Combinatory Categorial Grammar
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... Combinatory Categorial Grammar (CCG) is a strongly lexicalized theory of grammar in which grammatical categories consist of (a) a syntactic type defining valency (the number and syntactic type of its arguments, if any) and the type of the result, the left-right linear order of those arguments, and the order of their combination, together with (b) a logical form and (c) a phonological form. ...
Chapter 7 Quantification and Pronominal Anaphora
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Type raising, which we saw in the last chapter in its morphosyntactic aspect as a rule of the CCG lexicon, is also well known as the operation that Montague (1973) used in semantics to treat quantification in natural language and capture the phenomena of scope illustrated in example (1) of chapter 2, Somebody loves everybody, with which we began discussing quantifier-scope. It is standard ...
Part III Scope, Coordination, and Polarity
Chapter 8 Inverse Scope
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... Because certain universals, by contrast with the plural existentials, are genuine quantifiers, they and they alone can truly invert scope in both right- and left- branching derivations. For example, every can invert as follows (once again the left-branching inverting reading and the noninverting readings for both derivations are suggested as an exercise): ...
Chapter 9 Distributional Scope of Plurals
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It was noted in connection with example (26a) in chapter 4, repeated here, that the possibility of downward distribution of the nonspecific and counting existentials cannot arise from generalized quantifier semantics of the nominals, since they cannot in general invert scope. ...
Chapter 10 Coordination and Scope
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The distinction drawn in this book between true universal generalized quantifiers and generalized Skolem terms explains the asymmetry noted in section 2.2 in their respective patterns of interaction with syntactic coordination. The fact that universals distribute over and and not over or, as in (4) of chapter 2, repeated here, is simply a consequence of the standard generalized quantifier ...
Chapter 11 Negation and Polarity
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As we saw in part I, negation introduces complex issues of syntactic polarity marking and directionality of monotone inference. We were able to temporarily suppress these details in part II and the earlier chapters of part III by carefully choosing all examples for nonnegative polarity. However, the inclusion of negation forces certain decisions in the semantics. Moreover, polarity is of ...
Chapter 12 Related Approaches
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The present theory shares many features with other accounts mentioned in the preceding chapters—in particular, with the S´anchez Valencia/Dowty account of polarity, with various Choice Function–based accounts of the nonuniversal quantifiers, and with various referential theories. More specifically, it resembles a statically scoped form of DRT in which discourse referents are object ...
Part IV Applications and Conclusions
Chapter 13 Efficient Processing with CCG
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Many critics have assumed that, because CCG allows semantically equivalent alternate surface derivations typified by (10) and (11) in chapter 6, and because it allows English nounphrases to have all of the type-raised categories that a full-blown morphological case system would allow, this so-called spurious ambiguity must make it quite impracticable to apply CCG to useful tasks like ...
Chapter 14 Conclusion
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The preceding chapters imply that among the so-called quantifier determiners in English, the only ones that have interpretations corresponding to generalized quantifiers are those that engender dependency-inducing scope inversion, refuse to combine with collective predicates like gather in the library, have singular agreement only, and undergo distributive conjunction. These genuine ...
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Page Count: 324
Publication Year: 2011